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arXiv · 2403.02785

A Fully-discrete Semi-Lagrangian scheme for a price formation MFG model

Yuri Ashrafyan·Diogo Gomes
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Abstract

Here, we examine a fully-discrete Semi-Lagrangian scheme for a mean-field game price formation model. We show the existence of the solution of the discretized problem and that it is monotone as a multivalued operator. Moreover, we show that the limit of the discretization converges to the weak solution of the continuous price formation mean-field game using monotonicity methods. Numerical simulations demonstrate that this scheme can provide results efficiently, comparing favorably with other methods in the examples we tested.

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Yuri Ashrafyan, Diogo Gomes. 2025-01-30. A Fully-discrete Semi-Lagrangian scheme for a price formation MFG model. https://arxiv.org/abs/2403.02785

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